Liverpool qualified for the Champions League group stage, but only after being given a huge scare by AK Graz.
The Austrian side went ahead early in the second half through Mario Tokic's superb strike, which crossed the line after hitting Jerzy Dudek's bar.
Late on Tokic's finishing was less assured when the defender volleyed high over the bar following a Graz corner.
Liverpool's best effort in a hugely disappointing performance was a first-half Steven Gerrard shot.
Having fielded the same starting line-up in their last three competitive games, Liverpool manager Rafael Benitez made three changes, selecting Salif Diao, Stephane Henchoz and Darren Potter.
It was a debut for the 19-year-old Potter, who in build and style resembles Steve McMananman.
I have seen the video and he made a mistake
Even when Liverpool went a goal down Benitez resisted the temptation to introduce the experience of Dietmar Hamann and Igor Biscan to steady the nerves of the four-time European Cup winners, opting to deploy two other youngsters Stephen Warnock and Florent Sinama Pongolle.
Hamann did eventually come on - in the 90th minute - helping Liverpool survive three minutes of stoppage time.
Despite the sell-out crowd, Liverpool were unable to find their rhythm throughout the game.
As ever Gerrard seemed to be everywhere, while Milan Baros and Djibril Cisse were full of running in attack.
But Liverpool were unable to create many clear-cut openings, the best an early free-kick involving Kewell and Gerrard.
The Graz defence had been expecting a cross into the area, but Kewell pulled the ball for Gerrard, whose shot went narrowly wide.
The Austrian side also threatened from set-pieces, notably just before the interval when Roland Kollmann almost touched the ball home.
Soon after the restart Graz took the lead, again capitalising on Liverpool's defensive uncertainity from a set-piece.
Following a corner Tokic picked up the ball on the edge of the penalty area, flicked it over Kewell's head and then struck a superb shot past Dudek.
Tokic's goal prompted Benitez to withdraw the ineffectual Kewell and replace him with Warnock.
Gerrard also began to raise his game and his cross from the left almost found Baros at the far post.
Baros and Cisse then combined smartly, but the ball arrived too quickly for the Frenchman and his volley was well over.
Potter's chip into the box then found Baros and Cisse lurking unmarked, but the Czech Republic striker missed his kick, while Cisse's bicycle kick was imperfectly executed.
With Anfield becoming more and more hushed as the game continued, Graz continued to probe with Dudek having to save a Kollmann header.
During the game Spanish referee Luis Medina Cantalejo looked to have booked Graz captain Reen Aufhauser twice, but just like Andy D'Urso at the weekend, the Spaniard failed to bring out his red card.
Liverpool: Dudek, Carragher, Henchoz, Hyypia, Riise, Potter,
Gerrard, Diao, Kewell, Baros, Cisse.
Subs: Harrison, Finnan,
Hamann, Sinama Pongolle, Biscan, Warnock, Whitbread.
Liebherr GAK: Schranz, Standfest, Tokic, Pogatetz, Majstorovic,
Plassnegger, Sick, Aufhauser, Amerhauser, Kollmann, Bazina.
Subs: Ramusch, Muratovic, Almer, Sencar, Dollinger, Hassler,
Referee: Luis Medina Cantalejo (Spain).